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Functional Central Limit Theorem and Strong Law of Large Numbers for Stochastic Gradient Langevin Dynamics (2210.02092v2)

Published 5 Oct 2022 in math.PR, cs.LG, and math.OC

Abstract: We study the mixing properties of an important optimization algorithm of machine learning: the stochastic gradient Langevin dynamics (SGLD) with a fixed step size. The data stream is not assumed to be independent hence the SGLD is not a Markov chain, merely a \emph{Markov chain in a random environment}, which complicates the mathematical treatment considerably. We derive a strong law of large numbers and a functional central limit theorem for SGLD.

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